Occasionally while pushing hands with anybody, you hear interesting little comments made in passing that are useful probes to much deeper misunderstandings.
Such occurred the other day when I heard from a fairly experienced practitioner: "You Cheng Manqing [style] people always keep your hands kind of low, it leaves your head wide open" [meaning to say that I was unmindful of a vulnerability of which this person would never heaven forbid take unprincipled advantage, but which was a significant deficiency in the method.]
This reveals a number of common "nested" or "layered" misconceptions about push hands. First of all, push hands is not in any way a combative training drill! It is not meant to be that. Nor is it meant to be a safe simulation of such, or a substitute for such, or have any other direct connection to such. If it were intended as combative training there are far greater deficiencies that would glare out at you right from the starting gate, such as defending real estate (in fixed step practice) and many many others.
Push hands practice is related to eventual combative outcome in something of the way that physics students writing equations for electron orbits on a blackboard in a classroom in U of Chicago physics department is related to the actual detonation of Fat Man or Little Boy over a Japanese city.
You wouldn't (I hope) remonstrate with such students "Well your math seems to be alright yet there must be a mistake cause I don't see a mushroom cloud."
The Push Hands Drill of Tai Ji Quan is a diagnostic practice to identify tension in oneself and a partner and a developmental practice to foster skill in the application of internal energy to such identified tense zones to move the partner's entire body with a light physical touch.
The above is all it is. That's enough. It doesn't need to be anything more. So the "head" thing is obviously misguided. Yes, I don't "cover" or "protect" my head in push hands practice any more than I put on a bulletproof vest before brushing my teeth. In push hands we enter into a state of trust just as for example you and your dentist do when s/he works on you, neither of you is expected to punch the other and if either of you do that would be simple assault and battery and would have absolutely nothing to do with dentistry or the purpose of your original interaction.
Now, is there a time and place for learning how to protect your head (as part of a much larger project of learning realistic combatives) ? Of course there is! It's called boxing (or any number of other realistic or semi-realistic training programs). I have learned to protect my head very well in boxing, as you'll find if you box me or assault me outside our agreed interaction. But that skill has absolutely nothing to do with the purpose and practice of Push Hands in the Tai Chi context.
Push hands practice is about developing the ability to gently and easily yet powerfully, energetically, exploit perceived tension in a partner. (And of course it has nothing to do with structure, mechanics, anatomy or anything physical like that.) This light sensing skill could, down the road, have some kind of indirect relation to practical defensive outcomes, but within the immediate context of actual push hands practice, there is no relation whatsoever. It is a diagnostic tool for your own relaxation and sensitivity.
Because "deep unconscious tension" (the type I work with) is diffused throughout the partner's body, and it is immediately apparent and available to me from a single light touch to any part. Therefore I consciously and conscientiously choose to limit myself to the arms and upper torso only. No head. Why would I need to touch their head? Given my point that tension is diffused throughout their body, their arms or any part of their apart torso apart from head is just as good a "lever" or "handle" to move their entire body.
Conversely, if your level of skill is not yet capable of detecting the diffuse deep unconscious tension in their arms and/or upper torso (apart from neck and head) then why do you think you'll be able to sense it any better in those sensitive and injury prone areas (of neck and head)? Why not work on the main problem that is right in front of you rather than seeking some useless arcane (and annoying) byway or detour?
If you can sense tension properly you don't ever need to touch their head or neck to move them. If you cannot sense tension, touching their neck or head won't help you. And if you think to develop head-destroying martial combative skill through push hands, you're barking up the wrong tree in the first place. You could use an electric toothbrush to hammer a nail (or to beat somebody over the head) but why would you, given that (a) such misuse may damage the implement and (b) there are far better tools designed precisely for your actual purpose.
